are NOT like European and Japanese beech. They do not respond as quickly, nor as vigorously as those species to root or top pruning. They are VERY slow, conservative trees.
As such, aggressive collection kills them. I know, I've killed a few. I have one I collected about ten years ago that's worked up into a pretty decent bonsai. Along the way, I've learned that most American beech has diffuse root systems or are only clones of other nearby beech trees with only cursory root systems of their own.
This requires time be taken when collecting them. Ground layering and a two or even three year collection process is needed to get most out of the ground successfully.
Once in a container, things get even more complicated. A. beech throw only one spurt of spring growth. That's it. Ramification, therefore can take an eternity. Root pruning shouldn't be more frequent than every three or four years.
Don't be tempted to take advice from people who haven't worked with this particular species. Some of the more aggressive techniques used with Japanese and European beech will kill or greatly weaken the American species...